Concept Check Match each equation in Column I with its graph in C...

Question

Concept Check Match each equation in Column I with its graph in Column II.

I II
47. (x - 3)² + (y - 2)² = 25 A. 
48. B. 
49. C. 
50. D.

Accepted Answer

Hello, everyone. We are asked to identify the graph of the given equation. The equation we are given is the parentheses X minus seven squared plus the parentheses Y minus squared equals nine. We are provided a coordinate plane where the X and Y axis appear to have a scale of one. And we predominantly see the first quadrant looking at our given equation. First thing I recall is that this is very similar to the equation of a circle. So the equation of a circle is in parentheses, X minus H squared plus the parentheses Y minus K squared equals R squared. And I recall that the radius is R and that the center is the point HK. So here we again have the parentheses, X minus seven squared plus the parentheses, Y minus 13 squared equals nine. So I want to find the center. So H if we look at X minus H and compare it to X minus seven, they have the same sign. So this means H is seven for K, we have Y minus K and I compare it to Y minus 13, they have the same sign. So that means that K is a positive 13. So our center is the 0.7 13. So I'm gonna place that point on my graph. So I know it's the center of my circle and then I wanna find the radius. So the radius is R, so we can say R squared equals nine and define the radius will divide both sides by the, I'm sorry, we're gonna take the square root of both sides and that will tell me that R equals three. So our radius is three. So that means going from our center, I can go up three units and put a dot To the right three units, place a dot down three units and put a dot And to the left three units and put a dot These will be my guiding points to make my circle. So I'm going to graph the circle. It does not go through the center, it is the center. So it goes around it and I'm gonna try to make it as circ as I can. All right, doesn't look too bad. So we have a circle with a center at 7 13 and a radius of three have a nice day.

Concept Check Match each equation in Column I with its graph in Column II. I II 47. (x - 3)² + (y - 2)² = 25 A. 48. B. 49. C. 50. D.

Key Concepts

Circle Equation

Graphing Circles

Coordinate Plane

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